/*
Climbing Stairs
===============

You are climbing a stair case. It takes n steps to reach to the top.

Each time you can either climb 1 or 2 steps. In how many distinct ways can you climb to the top?

Example 1:
Input: 2
Output: 2
Explanation: There are two ways to climb to the top.
1. 1 step + 1 step
2. 2 steps

Example 2:
Input: 3
Output: 3
Explanation: There are three ways to climb to the top.
1. 1 step + 1 step + 1 step
2. 1 step + 2 steps
3. 2 steps + 1 step
 

Constraints:
1 <= n <= 45

Hint #1  
To reach nth step, what could have been your previous steps? (Think about the step sizes)
*/

class Solution
{
public:
  int climbStairs(int n)
  {
    if (n == 1)
      return 1;

    vector<int> dp(n + 1, 0);
    dp[1] = 1;
    dp[2] = 2;

    for (int i = 3; i <= n; i++)
      dp[i] = dp[i - 1] + dp[i - 2];
    return dp[n];
  }
};
